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abruzzese [7]
3 years ago
13

Which expression is equivalent to 4(7 + 8)?A) 11+8B) 11+12C) 28+12D) 28+32​

Mathematics
2 answers:
andreev551 [17]3 years ago
7 0
To do this we take the outlier off the parenthesis (the 4) and multiply it by the two numbers inside the parenthesis...

4*7 + 4*8

28+32
Vinil7 [7]3 years ago
4 0

Answer:

D) 28+32

Step-by-step explanation:

4(7+8)=4(15)=60

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If f(2) = 13 and f '(x) ≥ 3 for 2 ≤ x ≤ 4, how small can f(4) possibly be?
aniked [119]
The slope f'(x) = [f(4) - f(2)]/(4-2)≥3,
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8 0
3 years ago
What is the standard form of the equation of a line for which the length of the normal segment to the origin is 8 and the normal
jeka57 [31]
Slope of line = tan(120) = -tan(60) = - √3
Distance from origin = 8

Let equation be Ax+By+C=0
then -A/B=-√3, or
B=A/√3.
Equation becomes
Ax+(A/√3)y+C=0

Knowing that line is 8 units from origin, apply distance formula
8=abs((Ax+(A/√3)y+C)/sqrt(A^2+(A/√3)^2))
Substitute coordinates of origin (x,y)=(0,0)  =>
8=abs(C/sqrt(A^2+A^2/3))
Let A=1 (or any other arbitrary finite value)
solve for positive solution of C
8=C/√(4/3) => C=8*2/√3 = (16/3)√3

Therefore one solution is
x+(1/√3)+(16/3)√3=0
or equivalently
√3 x + y + 16 = 0

Check:
slope = -1/√3  .....ok
distance from origin
= (√3 * 0 + 0 + 16)/(sqrt(√3)^2+1^2)
=16/2
=8  ok.

Similarly C=-16 will satisfy the given conditions.

Answer  The required equations are
√3 x + y = ± 16 
in standard form.

You can conveniently convert to point-slope form if you wish.




4 0
3 years ago
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